Goodman and Kruskal Gamma in R

### gammaGK function
gammaGK <- function(x,y=NULL){
  concordant <- function(x){ 
    ## get sum(matrix values > r AND > c) 
    ## for each matrix[r, c] 
    mat.lr <- function(r,c){ 
      lr <- x[(r.x > r) & (c.x > c)] 
      sum(lr) 
    } 
    
    ## get row and column index for each 
    ## matrix element 
    r.x <- row(x) 
    c.x <- col(x) 
    
    ## return the sum of each matrix[r, c] * sums 
    ## using mapply to sequence thru each matrix[r, c] 
    sum(x * mapply(mat.lr, r = r.x, c = c.x)) 
  } 
  
  discordant <- function(x){ 
    ## get sum(matrix values > r AND < c) 
    ## for each matrix[r, c] 
    mat.ll <- function(r,c){ 
      ll <- x[(r.x > r) & (c.x < c)] 
      sum(ll) 
    } 
    
    ## get row and column index for each 
    ## matrix element 
    r.x <- row(x) 
    c.x <- col(x) 
    
    ## return the sum of each matrix[r, c] * sums 
    ## using mapply to sequence thru each matrix[r, c] 
    sum(x * mapply(mat.ll, r = r.x, c = c.x)) 
  } 
 
  if(is.table(x) | is.matrix(x)){
    c <- concordant(x) 
    d <- discordant(x)
    n <- sum(x)
  }
  else{
    tab <- table(x,y)
    c <- concordant(tab) 
    d <- discordant(tab)
    n <- sum(tab)
  }
  gamma <- (c - d) / (c + d)
  
  arg <- (c+d)/(n*(1-(gamma^2)))
  stdError <- 1/sqrt(arg)
  z <- gamma/stdError
  
  return(gamma)
}